"It is only one poll, but in a rather unexpected reverse of polling assumptions so far, both our phone poll and our online poll are consistent".

Once undecideds were excluded, both new polls gave 52 percent support for Brexit compared to 48 percent for "Remain".

In Tuesday's Daily Telegraph, Lynton Crosby — Cameron's campaign strategist at last year's general election — said an "increasing focus on lack of control over immigration" was key to what he said was a shifting mood.

"Leave" campaigners including former London mayor Boris Johnson last week seized on figures which put net migration into Britain at 333,000 last year to argue that it should pull out of the EU.

A poll of polls of the last six surveys maintained by the What UK Thinks academic project currently puts "Remain" on 51 percent and "Leave" on 49 percent.